rf315_projectpdf.C File Reference

Detailed Description

Multidimensional models: marginizalization of multi-dimensional pdfs through integration

 
#include "RooRealVar.h"
#include "RooDataHist.h"
#include "RooGaussian.h"
#include "RooProdPdf.h"
#include "RooPolyVar.h"
#include "TH1.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooNumIntConfig.h"
using namespace RooFit;
 
void rf315_projectpdf()
{
   // C r e a t e   p d f   m ( x , y )  =  g x ( x | y ) * g ( y )
   // --------------------------------------------------------------
 
   // Increase default precision of numeric integration
   // as this exercise has high sensitivity to numeric integration precision
   RooAbsPdf::defaultIntegratorConfig()->setEpsRel(1e-8);
   RooAbsPdf::defaultIntegratorConfig()->setEpsAbs(1e-8);
 
   // Create observables
   RooRealVar x("x", "x", -5, 5);
   RooRealVar y("y", "y", -2, 2);
 
   // Create function f(y) = a0 + a1*y
   RooRealVar a0("a0", "a0", 0);
   RooRealVar a1("a1", "a1", -1.5, -3, 1);
   RooPolyVar fy("fy", "fy", y, RooArgSet(a0, a1));
 
   // Create gaussx(x,f(y),sx)
   RooRealVar sigmax("sigmax", "width of gaussian", 0.5);
   RooGaussian gaussx("gaussx", "Gaussian in x with shifting mean in y", x, fy, sigmax);
 
   // Create gaussy(y,0,2)
   RooGaussian gaussy("gaussy", "Gaussian in y", y, 0.0, 2.0);
 
   // Create gaussx(x,sx|y) * gaussy(y)
   RooProdPdf model("model", "gaussx(x|y)*gaussy(y)", gaussy, Conditional(gaussx, x));
 
   // M a r g i n a l i z e   m ( x , y )   t o   m ( x )
   // ----------------------------------------------------
 
   // modelx(x) = Int model(x,y) dy
   RooAbsPdf *modelx = model.createProjection(y);
 
   // U s e   m a r g i n a l i z e d   p . d . f .   a s   r e g u l a r   1 - D   p . d . f .
   // ------------------------------------------------------------------------------------------
 
   // Sample 1000 events from modelx
   std::unique_ptr<RooAbsData> data{modelx->generateBinned(x, 1000)};
 
   // Fit modelx to toy data
   modelx->fitTo(*data, Verbose(), PrintLevel(-1));
 
   // Plot modelx over data
   RooPlot *frame = x.frame(40);
   data->plotOn(frame);
   modelx->plotOn(frame);
 
   // Make 2D histogram of model(x,y)
   TH1 *hh = model.createHistogram("x,y");
   hh->SetLineColor(kBlue);
 
   TCanvas *c = new TCanvas("rf315_projectpdf", "rf315_projectpdf", 800, 400);
   c->Divide(2);
   c->cd(1);
   gPad->SetLeftMargin(0.15);
   frame->GetYaxis()->SetTitleOffset(1.4);
   frame->Draw();
   c->cd(2);
   gPad->SetLeftMargin(0.20);
   hh->GetZaxis()->SetTitleOffset(2.5);
   hh->Draw("surf");
}

 
[#0] WARNING:InputArguments -- The parameter 'sigmax' with range [-inf, inf] of the RooGaussian 'gaussx' exceeds the safe range of (0, inf). Advise to limit its range.
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooRombergIntegrator to calculate Int(y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooRombergIntegrator to calculate Int(y)
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
[#1] INFO:Minimization --  The following expressions will be evaluated in cache-and-track mode: (gaussx)
[#0] WARNING:Minimization -- RooAbsMinimizerFcn::synchronize: WARNING: no initial error estimate available for a1: using 0.4
 
prevFCN = 1900.156536  a1=-1.488, 
prevFCN = 1899.96972  a1=-1.512, 
prevFCN = 1900.566064  a1=-1.499, 
prevFCN = 1900.127678  a1=-1.501, 
prevFCN = 1900.187622  a1=-1.484, 
prevFCN = 1899.958651  a1=-1.483, 
prevFCN = 1899.959674  a1=-1.484, 
prevFCN = 1899.958586  a1=-1.484, 
prevFCN = 1899.958651  a1=-1.483, 
prevFCN = 1899.959674  a1=-1.484, 
prevFCN = 1899.958586  a1=-1.483, 
prevFCN = 1899.958779  a1=-1.484, 
prevFCN = 1899.958562  a1=-1.484, 
prevFCN = 1899.958651  a1=-1.483, 
prevFCN = 1899.958779  a1=-1.484, 
prevFCN = 1899.958562  a1=-1.484, 
prevFCN = 1899.958674  a1=-1.484, 
prevFCN = 1899.95863  a1=-1.484, [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooRombergIntegrator to calculate Int(y)

Date

July 2008

Author

Wouter Verkerke

Definition in file rf315_projectpdf.C.